AbstractThis paper concerns itself with the problem of estimating the parameters of one‐way and two‐way classification models by minimization of the sum of the absolute deviations of the regression function from the observed points. The one‐way model reduces to obtaining a set of medians from which optimal parameters can be obtained by simple arithmetic manipulations. The two‐way model is transformed into a specially structured linear programming problem, and two algorithms are presented to solve this problem. The occurrence of alternative optimal solutions in both models is discussed, and numerical examples are pr